In the approximation of instantaneous reheating, we expect a reheating temperature \(T_{\rm rh} \sim 10^{14}\,\textrm {GeV}\)  in the relevant part of parameter space (see Fig. REF ).
Let us now consider the evolution of the primordial charges generated during axion inflation from this high temperature scale all the way down to the temperature scale of wash-in leptogenesis, \(T_{B-L}\) , which we assume to be of the order of a few 100 TeV in our benchmark scenario.
In doing so, it will be important to keep track of the subset of SM interactions that have already reached thermal equilibrium in dependence of the decreasing temperature of the thermal bath.
In order to facilitate the discussion, we will split the temperature range from \(T_{\rm rh}\)  to \(T_{B-L}\)  into five different regimes, each of which is characterized by a certain subset of SM interactions in equilibrium.
For more details on the equilibration temperatures of the individual SM Yukawa and sphaleron interactions, see Ref. [1]}.
A second simplification consists in the fact that we will neglect the chemical potentials of the three RHNs, \(\mu _{N_i}\) , in our discussion.
At \(T \gg M_i\) , these chemical potentials may temporarily obtain nonzero values.
Whether and when this happens is, however, a model-dependent question and depends on the rate of \(\Delta L = 1\)  scattering processes such as, e.g., \(N_i Q_3 \leftrightarrow \ell _\alpha t\) , and hence on the RHN Yukawa couplings, as well as on the thermal history of the RHN population.
Moreover, all effects caused by \(\mu _{N_i} \ne 0\)  at high temperatures will be reverted at lower temperatures anyway when the RHNs turn nonrelativistic and the \(\mu _{N_i}\)  are driven to zero by the RHN Majorana masses.
At the time of wash-in leptogenesis, when \(T \sim M_i\) , we can therefore safely work with \(\mu _{N_i} = 0\) .
The model-dependent time evolution of the three \(\mu _{N_i}\)  will not affect our conclusions and is thus irrelevant for our purposes.
